I had a similar problem with ACF 4.2.2, then i updated to 4.3.0 and it was fixed. See here:
http://support.advancedcustomfields.com/forums/topic/authors-cant-upload-from-front-end-form/
After a few days, and i don’t know why, i was getting the same problem again. This time i found that TML’s Themed Profiles module is causing this (which is weird because it was activated before).
This thread solved my problem, and it might help you:
http://wordpress.org/support/topic/solving-wp-media-upload-in-the-frontend-and-tml?replies=4#post-4851176
